Comparators

A digital logic component that compares two binary numbers.

Comparator

Equality Comparator

Outputs whether the two numbers are equal or not.

Outputs whether the two numbers are equal or less than or greater than.

Suppose the comparator takes in $A$ and $B$ . And the output $G$ denotes whether $A$ is greater than $B$ .

$G = A\overline{B}$

$E = AB + \overline{A}\cdot\overline{B}$

$L = \overline{A} B$

Let $x_i = A_i B_i + \overline{A_i}\cdot \overline{B_i} = \overline{A_i \oplus B_i}$ . $x_i$ denotes if $A_i = B_i$ .

G = \sum_{i=0}^{n-1} \Bigg(\bigg(\prod_{j=i+1}^{n-1}{x_j}\bigg) A_i\overline{B_i}\Bigg)

E = \prod_{i=0}^{n-1} {x_i}

L = \sum_{i=0}^{n-1} \Bigg(\bigg(\prod_{j=i+1}^{n-1}{x_j}\bigg) \overline{A_i}B_i\Bigg)

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September 13, 2026 1 min read

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